[math-fun] Playing with c = (a*b) mod (a+b)

Hello MathFun & SeqFans, Start S = 2, 9,... Next term is (2*9)mod(2+9) 18 mod 11 = 7 S = 2, 9, 7,... Next term is (9*7)mod(9+7) 63 mod 16 = 15 S = 2, 9, 7, 15,... Next term is (7*15)mod(7+15) 105 mod 22 = 17 S = 2, 9, 7, 15, 17,... Next term is (15*17)mod(15+17) 255 mod 32 = 31 S = 2, 9, 7, 15, 17, 31,... Next term is (17*31)mod(17+31) 527 mod 48 = 47 S = 2, 9, 7, 15, 17, 31, 47,... Does this end in a loop? If yes, is there another start which doesn't? Best, É.